The amplitude of $\frac{1 + \sqrt{3}i}{\sqrt{3} + i}$ is

If $z_1, z_2$ and $z_3, z_4$ are $2$ pairs of complex conjugate numbers,then $\arg \left( \frac{z_1}{z_4} \right) + \arg \left( \frac{z_2}{z_3} \right)$ equals

The amplitude of $\frac{1 + \sqrt{3}i}{\sqrt{3} - i}$ is

Find the modulus and the argument of the complex number $z = -1 - i \sqrt{3}$.

If $z$ is a complex number such that $|z| = 4$ and $\text{arg}(z) = \frac{5\pi}{6}$,then $z$ is equal to

If ${z_1}, {z_2} \in \mathbb{C}$,then $\text{amp}\left( \frac{z_1}{\bar{z}_2} \right) = $